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` `1. A 4 letter word is written down by taking letters from the word KANYAKUMARI. What is the chance of the word to be of all different letters?

2. A card is drawn from a pack of 52 cards. The card is then replaced and the pack is reshuffled. It is done 6 times. Find the chance that the cards drawn are 2 hearts, 2 diamonds & 2 blacks.

7 years ago

Dear Abhipsa

KANYAKUMARI =2 K +3 A + 1N + 1Y + 1U + 1M + 1R +1I

Case letter does not include A and K

total number of 4 letter word can be formed =^{6}C_{4}4!................1

total number of 4 letter word that has different letter can be formed =^{6}C_{4}4!................2

case letter include A but not K

total number of 4 letter word can be formed =1*^{6}C_{3}4! + 1*1*^{6}C_{2}4!/2! +1*1*1*^{6}C_{1}4!/3! ( when 1 A ,2A and 3A are included respestively)...............3

total number of 4 letter word that has different letter can be formed =1*^{ 6}C_{3}4! ...........4

case letter include K but not A

total number of 4 letter word can be formed =1*^{6}C_{3}4! + 1*1*^{6}C_{2}4!/2! +( when 1 K ,2K are included respestively).................5

total number of 4 letter word that has different letter can be formed =1*^{ 6}C_{3}4!...............6

case letter K and A both included

total number of 4 letter word can be formed =1*1*^{6}C_{2}4! + 1*2*^{6}C_{1}4!/2! + 1*3*^{6}C_{0}4!/3!+2*1*^{6}C_{2}4!/2!+2*2*^{6}C_{0}4!/2!2!( when 1 K 1A ,1K2A,1K3A,2k1A,2K 2A are included respestively).................7

total number of 4 letter word that has different letter can be formed =1*1*^{ 6}C_{2}4!...............8

so pobability =(2+4+6+8)/(1+3+5+7)

put value of above equation and calculate

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Badiuddin

7 years ago

Thank you for the answer. Please answer the second question also.

7 years ago

Thank you for your answer. Please answer the second question that i've posted.

7 years ago

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